Straight Line and Circular Arc Methods for Developing G1 and G2 Involute Curves

Parametric polynomial curves such as Bezier, Ball, B-splines, Non-uniform B-splines (NURBS) are used for free form curve design. In this paper, we classify these curves as conventional curves. The flexibility of these curves deems suitable for use in the interactive design of curves. On the contrary, these curves cannot be used for highways, railways and robot trajectory designs as the signed curvature of these curves are difficult to control. As a result, the designer has to integrate a time consuming fair process. There are unconventional curves with easy control of the curvature namely, Euler and equiangular spirals. Unfortunately, the formulation of these spirals involves Fresnal integral and exponential functions respectively, which results in extra overhead and implementation. This paper introduces two type of curves which are generated from an evolute- involute process. The first type of involute curve(s) is generated using straight line(s) as the evolute(s) and named IFSL. The second type of involute curve(s) is generated based on circular arc(s) and a straight line and named IFCA.